Lux Investing
How do you set up this Linear Programming Problem?
A couple with $20,000 decides to invest in two types of bonds: those yielding 5% and those yielding 12%. The amount invested in the higher yield bonds will not exceed the amount invested in the lower yield bonds. Three times the low-risk investment plus the high-risk investment should not exceed $50,000. What is the optimal investment strategy? What is the maximum annual return?
Public Comments
- H=amount is high-yield L=amount in low yield H+L=20000 3L+H=50000 Solve for H and L and compute return. ----- Concerning the = vs <=: As it's worded, yes, the <= is the literal translation, but since the goal is to maximize return, there's no need to consider the "less than" case.
- He's right. I would like to note two things... should not exceed means <= (doesn't really make a diff here), and the maximum annual return will be where the graphs cross. Solve the equality for H (or L) and substitute into the inequality. Then back substitute and determine the return. I don't THINK you'll need calculus the way the problem is stated. You didn't say anything about compound interest etc. The way the problem is worded you have to make some assumptions. The final return is going to be 50k because you didn't specify a time limit. Is there more to this problem? So you have to figure out the end value of the accounts and divide by the annual return, which you know from 3L + H = 20K and of course the time it takes will be from I = PRT thus: [3L(.05) + H(.12)] t = 30K and then you can figure the annual return. My communication skills are a bit fuzzy at best but I think that will get you there.
